Answered

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The circle below has center E. Suppose that m

The Circle Below Has Center E Suppose That M class=
The Circle Below Has Center E Suppose That M class=

Sagot :

Answer:

(a) mFG = 108°

(b) m∠FEG = 108°

Explanation:

Since FH is tangent to the circle, the angle EFG can be calculated as follows:

∠EFG + ∠GFH = 90°

So, replacing the measure of ∠GFH, we can calculate ∠EFG as:

∠EFG + 54° = 90°

∠EFG = 90° - 54°

∠EFG = 36°

Now, the triangle formed by points E, G, and F is isosceles because the length of EF is equal to the length of EG. It means that the ∠EFG has the same measure as ∠EGF, so we can calculate the measure of ∠FEG as:

∠EFG + ∠EGF + ∠FEG = 180°

Because the sum of the interior angles of a triangle is 180°-

So, replacing ∠EFG and ∠EGF by 36°, we get:

36° + 36° + ∠FEG = 180°

72° + ∠FEG = 180°

∠FEG = 180° - 72°

∠FEG = 108°

Therefore, the answers are:

(a) mFG = 108°

(b) m∠FEG = 108°

Because the measure of the arc FG is the same measure of ∠FEG.

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